Title:Substantive Syllogisms

J. A. Novak’s “Substantive Syllogisms”

Title:Substantive Syllogisms

Author:Joseph A. Novak

Commentary:R. Yanal

 2003 Joseph A. Novak

Introduction

Treatment of the syllogism as a basic form of inference is something found to be widespread, even today, in the post twentieth century which saw the entrenchment of classical propositional logic and the appearance of various post-classical logics. A survey of logic texts seems to reveal that the authors have generally followed a standard presentation of the syllogism. Syllogisms are often described as arguments illustrating class relationships and hence it is not uncommon to find that Venn diagramming techniques are discussed in conjunction with them. The examples and exercises connected with the syllogistic form of inference tend to be rather obvious and humdrum ones where certain classes of things are seen as subordinate or superordinate to others and are either included or excluded from them. This practice has a long history; indeed, one can argue that Aristotle himself paved the way for this sort of interpretation. A survey of the classic and quite elegant establishment of the valid moods of the syllogism in Prior Analytics I, 4-7 shows him providing "values" for "variables" that seem to follow this sort of inclusion. This interpretation seems to be especially attractive when he is dealing with the so-called cases of "contrasted instances" (Ross 1949, 300 ff.) – such terms as "man" "horse" and "animal"; "horse" "swan" and "white"; and "stones" "animals" and "lines" illustrate how factual relationships of inclusion or exclusion between the groups designated by these terms render invalid certain moods (See Appendix). This method is not restricted only to the first figure, as is clear from its employment beyond the fourth chapter of the Prior Analytics (where the first figure is developed).

It is probably quite easy to find any number of teachers who find this approach to the syllogism uninteresting and a large number of students who consider it boring. The syllogistic is thought to be acknowledged by Aristotle as his own innovative discovery,[1] and of such the author could be rightly proud in surveying its intricate and concise development in the section of the Prior Analytics already noted. However, such a pride seems even more warranted if the syllogism is taken to be of greater use than simply portraying class relations. Perhaps, to put it in another way, if the philosophical enterprise itself is interested in more than just taxonomy,[2] the syllogism itself will have to do more than simply classify in order to function in this broader enterprise as a respectable philosophical tool. Indeed, if the syllogism has antedated Aristotle as an applied method in philosophy – even if not elaborated in the format he had provided in the Prior Analytics – one would suspect that it might be of some significance. Although the vast majority of textbook treatments of the syllogism contain the perfunctory class analysis noted, it is easy to find such books exemplifying other reasoning forms (reductios, conditional arguments, etc.), even if these are also displayed by equally uninteresting and standard (and not infrequently plagiarized?) examples. A notable exception is R. Purtill who tries to provide substantive philosophical arguments as exemplifications of reasoning forms. How widespread the reception of his text has been is difficult for me to say; one possible drawback to a wide audience is the employment of non-standard symbolic notation. However, he employs a huge number of interesting philosophical arguments drawn from the texts of major philosophers (Descartes, Leibniz, Hume, etc.), arguments on key issues of the respective philosophers or historical periods in which they lived. Nonetheless, the very section of his text dealing with the syllogistic shows the same limited approach and artificiality of examples, e.g., he utilizes some of Lewis Carroll's material (1897 and 1887) that has been the basis of many other texts, directly or indirectly.

The purpose of this paper is to provide an historical view of the employment of syllogistic reasoning that will be both of intrinsic interest in showing how that format has been employed in arguments on important matters and of pedagogic interest in highlighting samples for engaging instances of that format of argument for beginners in logic. In effect, rather than the stereotypical instances of syllogisms, the paper will try to put forward "substantive syllogisms", i.e., syllogisms that deal with matters of some import for different areas of philosophy. The historical survey will also show how the syllogism was able to function creatively to explore exegetically the nature of arguments proposed by philosophers and even creatively provide expansions of those arguments and justifications for some of the claims made within them.

Historical Survey

Although Aristotle is the figure who has left us a detailed method of deductive reasoning in his syllogistic, one does not thereby want to make the claim that he was the first philosopher to utilize it as an inference form. E. de Strycker, while maintaining that Aristotle's claim in the Sophistical Refutations of originality in logic was to be applied to the development of the syllogism (1932),[3] nonetheless examined claims that the initial use of the syllogism can be seen in Plato. The claims he examines are from more modern authors such as Ritter, as well as earlier authors in the Byzantine and Renaissance traditions such as Plethon, Scholarios, Trebizond, and Bessarion. The first and last of these earlier authors claim that Aristotle was not an innovator, while the other two authors championed his originality. Bessarion actually lists a number of syllogisms to be found in Plato (especially the Parmenides and the Timaeus). De Strycker (1932, 56) concludes his own analysis by asserting that this older tradition maintained that Aristotle had discovered the theory of the syllogism and Plato had employed it – but that these two claims were left without proper elaboration and integration.

He proceeds to examine in more detail how these claims stand in light of the original texts of Plato by examining some examples of syllogistic reasoning in Plato.[4] Consider the first that he offers from Phaedo 105e2-7, a passage which reads:

"What do we call something which is not able to receive in itself death?

"Non-mortal"

"The soul is not able to receive in itself death?"

"No."

"The soul then is a non-mortal thing?"

"A thing non-mortal."

Now there are two things to note with regard to this passage. First, it is in a dialogue format, a format, moreover, which includes statements other than purely declarative ones, i.e., interrogative ones. Second, there are not the quantifiers that seem prerequisite for any syllogism. Now, with regard to the first point, one might say that, as important as the dialogue form is to Plato both in extent (across most of his works) and in intent (his Seventh Letter's emphasis on it), one can argue that there is a core of reasoning that can be extracted from the conversation format. Translators have been known to leave out the interlocutors remarks and (rhetorical/leading) questions can be turned into straightforward assertions.[5] Given other minor alterations, one can arrive at the following syllogism:

Anything that is not able to receive into itself death is non-mortal

The soul is not able to receive into itself death.

THEREFORE, the soul is non-mortal.

This now has the appearance of a Barbara syllogism. Another example is cited from Republic I (353b2-7) and put forward as:

"Does not everything which has a particular function also have an excellence which is proper to it?"

"Do not eyes, as we say, have their function?"

"Yes."

"Then they also have an excellence which is proper to them."

Eliminating the interrogative negatives here, one ends up with a Barbara syllogism. However, a glance at the context of this passage shows that the major premise is not given as an established universal under which particular cases are to be subsumed for a deductive conclusion, but rather that it is proposed as a universal and the particular cases which Plato goes on to mention, i.e., eyes and ears, are meant to establish it. In other words, here there seems to be an induction rather than a deduction at work, albeit when taken in part, as is done above, another Barbara syllogism seems to appear.

Another syllogism noted by de Strycker in Lutoslawski's work (1897, 203) is said to be found in the Charmides 161. The passage reads:

"So it seems that modesty both is and is not a good."

"Yes, it does."

"But temperance must be good if it makes those good in whom it is present and makes bad those in whom it is not."

"Why yes, it seems to me to be exactly as you say."

"Then temperance would not be modesty if it really is a good and if modesty is no more good than bad."

Clearly, one must make the same concession as earlier in overlooking the dialogue format. In addition, one must make more radical adjustments to bring its core into syllogistic form, i.e., the conditionals must be eliminated or transformed and the conjunctive contradictory predication must be reduced to a single negative predication.[6] Once these adjustments are made, the syllogism seems to emerge:

Modesty is not good.

Temperance is good.

THEREFORE, temperance is not modesty.

This, both Lutoslawski (and DeStrycker, it seems) would maintain is a Cesare, second figure. Of course, the appropriate universal quantifiers need to be inserted.

A further passage is taken from Philebus 54c:

"Now pleasure, since it is a process of generation, necessarily comes to be for the sake of some being."

"Of course."

"But that for the sake of which what comes to be for the sake of something comes to be in each case, ought to be put into the class {moira} of the things good in themselves, while that comes to be for the sake of something else belongs in another class {moira}, my friend."

"Undeniably."

"But if pleasure really is a process of generation, will we be placing it correctly, if we put it in a class different from that of the good?"

'That too is undeniable."

One seems to come to the following syllogism, in de Strycker's words (translated):

That which occurs in light of some thing cannot be entered in the class of the good.

Pleasure, insofar as it is a becoming, occurs in light of some thing.

THEREFORE, pleasure cannot be entered into the class of the good.

There must be some adjustments to get this syllogism into the form of the purely assertoric type (elimination of the modal elements) and there must also be the elimination of the metatheoretic description of the relationship ("class of"). Of course, the syllogism is often seen to be a device to explore or express class relationships, and Plato's use of the term "moira" seems to imply a conception suggestive of such division. When all this is taken into account, one seems to be confronted with a syllogism that could be a first figure Celarent.

De Strycker raises some other instances but they seem to require even more adaptation, due either to their enthymematic structure or to various complexities of formulation we noted above. As he himself notes, the form is often quite free.[7] There are other questions to be raised with regard to Plato's relationship to the syllogism -- some important ones are mentioned by DeStrycker. Plato seems to have no narrow technical use for the related terms syllogismos and syllogizesthai. The latter can mean "compare," "calculate," as well as "infer"; the former seems not to refer to a particular form of reasoning but rather to the act of inference.[8] Furthermore, Plato either lacks the terms such as protasis (premise) and akra (extremes) and horos (term) or he employs them in a way that display none of the technical implications that we find in the Aristotelian syllogistic.

Now, it is not surprising that Plato would have some forms of reasoning that, albeit not formulated in rigid syllogistic format, can be readily reducible to that format nonetheless. After all, the syllogism is not an "invention" of Aristotle, it is presumably just a discovery; the human mind does naturally – and, as it appears, quite frequently – engage in this form of reasoning. It would be intriguing to explore the dialogues carefully to assemble more examples of syllogisms themselves or of inferences which are more or less readily reducible to syllogisms. This exploration would yield a larger pool for pedagogic purposes.

In turning from Plato to Aristotle, one is clearly confronted with scores of inferences explicitly identified as syllogisms. A mere perusal of the Prior and Posterior Analytics provides ample support in favor of this claim. Moreover, Aristotle seems to think that all types of reasoning can be reduced to the syllogistic form (Prior Analytics I, 41b1-3). However, he employs all sorts of inferences that do not seem -- easily or even at all – reducible to the syllogistic form. Consider, for instance, an argument he uses in the Physics 217b29-218a8, which bears on the reality of time. After asking whether time exists or not and what is its nature, he then goes on to say:

"To start, then: the following considerations would make one suspect that it either does not exist at all or barely, and in an obscure way. One part of it has been and is not, while the other is going to be and is not yet. Yet time -- both infinite time and any time you like to take -- is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality.

Further, if a divisible thing is to exist, it is necessary that, when it exists, all or some of its parts must exist. But of time some parts have been, while others have to be, and no part of it is, though it is divisible. For what is 'now' is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of 'nows'."

Clearly, this argument is not given in a syllogistic format and trying to reformulate it into even a series of syllogisms would prove difficult. The Appendix provides an approximate reformulation in terms of a derivation format familiar from the propositional calculus. This presentation is, again, a rather rough formalization of one of Aristotle's arguments against the existence of Time; Aristotle will go on to consider a number of other arguments such as this, before presenting his own arguments in support of the existence of Time. The whole discussion in the Physics, however, employs arguments which are not, for the most part, syllogistic in form and surely not instances of his ideal model of demonstration. That Aristotle does employ syllogistic arguments is not under dispute. However, the numerous formulations of these, as in the Posterior Analytics where Aristotle tries to exemplify principles of his "philosophy of science" by means of syllogistic arguments, often have a content that is too abstruse for a pedagogic context. Still, within the Aristotelian tradition, the commitment to the syllogism and the exploration of arguments through the syllogistic form become very important, not only within the commentary tradition but also outside of it. Rather than viewing Aristotle's application of the syllogism within the confines of his own text, then, the paper will explore the syllogistic exegesis of his text that occurs later. Given the size constraints of this paper, I want to focus on the use that Thomas Aquinas makes of the syllogism to explore and develop Aristotle's ideas about a doctrine found in a familiar passage from the first book of the Nicomachean Ethics.

"If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall we not, like archers who have a mark to aim at, be more likely to hit upon what is right? If so, we must try, in outline at least, to determine what it is, and of which of the sciences or capacities it is the object. It would seem to belong to the most authoritative art and that which is most truly the master art. And politics appears to be of this nature; for it is this that ordains which of the sciences should be studied in a state, and which each class of citizens should learn and up to what point they should learn them; and we see even the most highly esteemed of capacities to fall under this, e.g. strategy, economics, rhetoric; now, since politics uses the rest of the sciences, and since, again, it legislates as to what we are to do and what we are to abstain from, the end of this science must include those of the others, so that this end must be the good for man. For even if the end is the same for a single man and for a state, that of the state seems at all events something greater and more complete whether to attain or to preserve; though it is worth while to attain the end merely for one man, it is finer and more godlike to attain it for a nation or for city-states. These, then, are the ends at which our inquiry aims, since it is political science, in one sense of that term" EN, I, 1094a18-1094b11.

Now, those familiar with Aquinas' commentaries recognize that he divides the text of Aristotle into lectiones (readings) upon which he then performs an exegesis. These lectiones vary in length. The selection here is the second lectio in his commentary and is highly illustrative of the impact of the syllogism in his commentary style. The first thing that Aquinas does is to disengage the primary propositions that are present in this section or pericope of text. They are, he says, three (which I will list as A1, A2, A3):